A mass weighting 64 pounds, attached to the end of a spring and stretches the spring 0.32 foot. There is no damping and no external forces acting on the system. The mass is initially released from a point 8 inches above the equilibrium position with a downward velocity of 5 ft/s.

a) Find the displacement at any time t, ut) (find the equation of motion)

b) What are the amplitude and period of motion?

c) How many complete cycles will the mass have completed at the end of 37 seconds?

d) At what time does the mass pass through the equilibrium position heading downward at the second time?

e) At what times does the mass attain its extreme displacements on either side of the equilibrium position?

f) What is the position of the mass at t-3 sec?

g) What is the instantaneous velocity at t-3 sec?

h) What is the acceleration at t=3sec?

i) What is the instantaneous velocity at the time when the mass passes through the equilibrium position?

j) At what time is the mass 5 inches below the equilibrium position?

k) At what time is the mass 5 inches below the equilibrium position heading in the upward direction?